Active probe for an atomic force microscope and method of use thereof

ABSTRACT

An AFM that combines an AFM Z position actuator and a self-actuated Z position cantilever (both operable in cyclical mode and contact mode), with appropriate nested feedback control circuitry to achieve high-speed imaging and accurate Z position measurements. A preferred embodiment of an AFM for analyzing a surface of a sample includes a self-actuated cantilever having a Z-positioning element integrated therewith and an oscillator that oscillates the self-actuated cantilever at a frequency generally equal to a resonant frequency of the self-actuated cantilever and at an oscillation amplitude generally equal to a setpoint value. The AFM includes a first feedback circuit nested within a second feedback circuit, wherein the first feedback circuit generates a cantilever control signal in response to vertical displacement of the self-actuated cantilever during a scanning operation, and the second feedback circuit is responsive to the cantilever control signal to generate a position control signal. A Z position actuator is also included within the second feedback circuit and is responsive to the position control signal to position the sample. In operation, preferably, the cantilever control signal alone is indicative of the topography of the sample surface. In a further embodiment, the first feedback circuit includes an active damping circuit for modifying the quality factor (“Q”) of the cantilever resonance to optimize the bandwidth of the cantilever response.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to atomic force microscopes (AFMs) and,particularly, to an AFM and method of use thereof that combines an AFM Zposition actuator and a self-actuated cantilever to provide high qualityimages at greatly increased imaging rates.

2. Description of the Related Art

An Atomic Force Microscope (“AFM”), as described in U.S. Pat. No.RE34,489 to Hansma et al. (“Hansma”), is a type of scanning probemicroscope (“SPM”). AFMs are high-resolution surface measuringinstruments. Two general types of AFMs include contact mode (also knownas repulsive mode) AFMs, and cyclical mode AFMs (periodically referredto herein as TappingMode™ AFMs). (Note that TappingMode™ is a registeredtrademark of Veeco Instruments, Inc. of Plainview, N.Y.)

The contact mode AFM is described in detail in Hansma. Generally, thecontact mode AFM is characterized by a probe having a bendablecantilever and a tip. The AFM operates by placing the tip directly on asample surface and then scanning the surface laterally. When scanning,the cantilever bends in response to sample surface height variations,which are then monitored by an AFM deflection detection system to mapthe sample surface. The deflection detection system of such contact modeAFMs is typically an optical beam system, as described in Hansma.

Typically, the height of the fixed end of the cantilever relative to thesample surface is adjusted with feedback signals that operate tomaintain a predetermined amount of cantilever bending during lateralscanning. This predetermined amount of cantilever bending has a desiredvalue, called the setpoint. Typically, a reference signal for producingthe setpoint amount of cantilever bending is applied to one input of afeedback loop. By applying the feedback signals generated by thefeedback loop to an actuator within the system, and therefore adjustingthe relative height between the cantilever and the sample, cantileverdeflection can be kept constant at the setpoint value. By plotting theadjustment amount (as obtained by monitoring the feedback signalsapplied to maintain cantilever bending at the setpoint value) versuslateral position of the cantilever tip, a map of the sample surface canbe created.

The second general category of AFMs, i.e., cyclical mode or TappingMode™AFMs, utilize oscillation of a cantilever to, among other things, reducethe forces exerted on a sample during scanning. In contrast to contactmode AFMs, the probe tip in cyclical mode makes contact with the samplesurface or otherwise interacts with it only intermittently as the tip isscanned across the surface. Cyclical mode AFMs are described in U.S.Pat. Nos. 5,226,801, 5,412,980 and 5,415,027 to Elings et al.

In U.S. Pat. No. 5,412,980, a cyclical mode AFM is disclosed in which aprobe is oscillated at or near a resonant frequency of the cantilever.When imaging in cyclical mode, there is a desired tip oscillationamplitude associated with the particular cantilever used, similar to thedesired amount of cantilever deflection in contact mode. This desiredamplitude of cantilever oscillation is typically kept constant at adesired setpoint value. In operation, this is accomplished through theuse of a feedback loop having a setpoint input for receiving a signalcorresponding to the desired amplitude of oscillation. The feedbackcircuit servos the vertical position of either the cantilever mount orthe sample by applying a feedback control signal to a Z actuator so asto cause the probe to follow the topography of the sample surface.

Typically, the tip's oscillation amplitude is set to be greater than 20nm peak-to-peak to maintain the energy in the cantilever arm at a muchhigher value than the energy that the cantilever loses in each cycle bystriking or otherwise interacting with the sample surface. This providesthe added benefit of preventing the probe tip from sticking to thesample surface. Ultimately, to obtain sample height data, cyclical modeAFMs monitor the Z actuator feedback control signal that is produced tomaintain the established setpoint. A detected change in the oscillationamplitude of the tip and the resulting feedback control signal areindicative of a particular surface topography characteristic. Byplotting these changes versus the lateral position of the cantilever, amap of the surface of the sample can be generated.

Notably, AFMs have become accepted as a useful metrology tool inmanufacturing environments in the integrated circuit and data storageindustries. A limiting factor to the more extensive use of the AFM isthe limited throughput per machine due to the slow imaging rates of AFMsrelative to competing technologies. Although it is often desirable touse an AFM to measure surface topography of a sample, the speed of theAFM is typically far too slow for production applications. For instance,in most cases, AFM technology requires numerous machines to keep pacewith typical production rates. As a result, using AFM technology forsurface measurement typically yields a system that has a high cost permeasurement. A number of factors are responsible for these drawbacksassociated with AFM technology, and they are discussed generally below.

AFM imaging, in essence, typically is a mechanical measurement of thesurface topography of a sample such that the bandwidth limits of themeasurement are mechanical ones. An image is constructed from a rasterscan of the probe over the imaged area. In both contact and cyclicalmode, the tip of the probe is caused to scan across the sample surfaceat a velocity equal to the product of the scan size and the scanfrequency. As discussed previously, the height of the fixed end of thecantilever relative to the sample surface can be adjusted duringscanning at a rate typically much greater than the scanning rate inorder to maintain a constant force (contact mode) or oscillationamplitude (cyclical mode) relative to the sample surface.

Notably, the bandwidth requirement for a particular application of aselected cantilever is generally predetermined. Therefore, keeping inmind that the bandwidth of the height adjustment (hereinafter referredto as the Z-axis or Z-position bandwidth) is dependent upon the tipvelocity as well as the sample topography, the required Z-positionbandwidth typically limits the maximum scan rate for a given sampletopography.

Further, the bandwidth of the AFM in these feedback systems is usuallylower than the open loop bandwidth of any one component of the system.In particular, as the 3 dB roll-off frequency of any component isapproached, the phase of the response is retarded significantly beforeany loss in amplitude response. The frequency at which the total phaselag of all the components in the system is large enough for the loop tobe unstable is the ultimate bandwidth limit of the loop. When designingan AFM, although the component of the loop which exhibits the lowestresponse bandwidth typically demands the focus of design improvements,reducing the phase lag in any part of the loop will typically increasethe bandwidth of the AFM as a whole.

With particular reference to the contact mode AFM, the bandwidth of thecantilever deflection detection apparatus is limited by a mechanicalresonance of the cantilever due to the tip's interaction with thesample. This bandwidth increases with the stiffness of the cantilever.Notably, this stiffness can be made high enough such that the mechanicalresonance of the cantilever is not a limiting factor on the bandwidth ofthe deflection detection apparatus, even though increased imaging forcesmay be compromised.

Nevertheless, in contact mode, the Z position actuator still limits theZ-position bandwidth. Notably, Z-position actuators for AFMs aretypically piezo-tube or piezo-stack actuators which are selected fortheir large dynamic range and high sensitivity. Such devices generallyhave a mechanical resonance far below that of the AFM cantilever broughtin contact with the sample, typically around 1 kHz, thus limiting theZ-position bandwidth.

Manalis et al. (Manalis, Minne, and Quate, “Atomic force microscopy forhigh speed imaging using cantilevers with an integrated actuator andsensor,” Appl. Phys. Lett., 68 (6) 871-3 (1996)) demonstrated thatcontact mode imaging can be accelerated by incorporating the Z positionactuator into the cantilever beam. A piezoelectric film such as ZnO wasdeposited on the tip-side of the cantilever. The film causes thecantilever to act as a bimorph such that by applying a voltage dependentstress the cantilever will bend. This bending of the cantilever, throughan angle of one degree, or even less, results in microns ofZ-positioning range. Further, implementing the Z-position actuator inthe cantilever increases the Z-position bandwidth of the contact modeAFM by more than an order of magnitude.

Nevertheless, such an AFM exhibits new problems with the Z-positioningwhich were not concerns with other known AFMs. For instance, the rangeof the Z actuator integrated with the cantilever is less than isrequired for imaging many AFM samples. In addition, because thepositioning sensitivity of each cantilever is different, the AFMrequires recalibration whenever the probe is changed due to a worn orbroken tip. Further, the sensitivity in some cases exhibits undesirablenon-linearity at low frequencies. These problems can make the Z actuatorintegrated with the cantilever a poor choice for general use as the Zactuator in commercial AFMs.

Furthermore, notwithstanding the above, in many AFM imagingapplications, the use of contact mode operation is unacceptable.Friction between the tip and the sample surface can damage imaged areasas well as degrade the tip's sharpness. Therefore, for many of theapplications contemplated by the present invention, the preferred modeof operation is cyclical mode, i.e., TappingMode®. However, thebandwidth limitations associated with cyclical mode detection aretypically far greater than those associated with contact mode operation.

In cyclical or non-continuous contact mode operation, the AFM cantileveris caused to act as a resonant beam in steady state oscillation. When aforce is applied to the cantilever, the force can be measured as achange in either the oscillation amplitude or frequency. One potentialproblem associated with cyclical mode operation is that the bandwidth ofthe response to this force is proportional to 1/Q (where Q is the“quality factor” of the natural resonance peak), while the forcesensitivity of the measurement is proportional to the Q of the naturalresonance peak. Because, in many imaging applications, the bandwidth isthe primary limiting factor of scan rate, the Q is designed to be low toallow for increased imaging speeds. However, reducing the Q of thecantilever correspondingly reduces force detection sensitivity, whichthereby introduces noise into the AFM image.

A further contributing factor to less than optimal scan rates incyclical mode operation is the fact that the amplitude error signal hasa maximum magnitude. Over certain topographical features, a scanning AFMtip will pass over a dropping edge. When this occurs, the oscillationamplitude of the cantilever will increase to the free-air amplitude,which is not limited by tapping on the surface. The error signal of thecontrol loop is then the difference between the free-air amplitude andthe setpoint amplitude. In this instance, the error signal is at amaximum and will not increase with a further increase in the distance ofthe tip from the sample surface. The topography map will be distortedcorrespondingly.

Finally, the maximum gain of the control loop in cyclical mode islimited by phase shifts, thus further limiting the loop bandwidth. Inview of these drawbacks, the Z-position measurement for an atomic forcemicroscope is typically characterized as being slew rate limited by theproduct of the maximum error signal and the maximum gain.

As a result, AFM technology posed a challenging problem if the scan ratein cyclical mode was to be increased significantly. One general solutionproposed by Mertz et al. (Mertz, Marti, and Mlynek, “Regulation of amicrocantilever response by force feedback,” Appl. Phys. Lett. 62 (19)at 2344-6 (1993)) (hereinafter “Mertz”), but not directed to existingcyclical mode AFMs, included a method for decreasing the effective Q ofa cantilever while preserving the sensitivity of the natural resonance.In this method, a feedback loop is applied to the cantilever resonancedriver such that the amplitude of the driver to the cantilever ismodified based on the measured response of the cantilever. Thistechnique serves to modify the effective Q of the resonating cantileverand will be referred to hereinafter as “active damping.” Mertzaccomplished active damping by thermally exciting the cantilever byfirst coating the cantilever with a metal layer that had differentthermal expansion properties than the cantilever beam itself. Then, inresponse to the feedback signals, Mertz modulated a laser incident onthe cantilever, so as to apply a modified driving force.

Unfortunately, this scheme is not practical to implement in existingcyclical mode AFMs. In a typical AFM of this type, the cantileverextends from a substrate which is mounted mechanically to apiezo-crystal used to drive the cantilever at its resonance. Thecantilever is driven at its resonance either by vibrating the substratewith the piezo-crystal, or by replacing the substrate with a mechanicalmounting structure which integrates the piezo-crystal and then excitingthe piezo-crystal to drive the cantilever. When active damping isapplied to such a structure, mechanical resonances other than that ofthe cantilever are excited and the gain of the active damping feedbackcannot be increased enough to significantly modify the effectivecantilever Q. Further, the Mertz design is prohibitively complex andinflexible for systems contemplated by the present invention due to thefact that, among other things, the modulating laser only deflects thecantilever in one direction. This introduces a frequency doubling effectthat must be accounted for in processing the output. Overall, inaddition to being directed to contact mode AFMs, the Mertz system iscomplex and produces marginally reliable measurements at undesirablyslow speeds.

Overall, the field of AFM imaging was in need of a system which isoperable in both contact and cyclical mode and which realizes highquality images at fast imaging speeds. In particular, with regard tocyclical mode AFMs, a system is desired that can modify the effective Qof a resonating cantilever with active damping without excitingmechanical resonances other than that of the cantilever. As a result,the system should optimize the Z-position bandwidth of the cantileverresponse to maximize scanning/imaging speeds, yet preserve instrumentsensitivity.

OBJECT AND SUMMARY

The present invention combines an AFM Z position actuator and aself-actuated Z-position cantilever (both operable in cyclical mode andcontact mode), with appropriately nested feedback control circuitry toachieve high-speed imaging and accurate Z-position measurements. Mostgenerally, the feedback signals applied to each of the actuators can beindependently monitored to indicate the topography of the samplesurface, depending upon the scan rate and sample topography.

In one embodiment of the present invention, the lower frequencytopography features of a sample, including the slope of the samplesurface, are followed by a standard Z actuator while the high frequencycomponents of the surface topography are followed by the self-actuatedcantilever. Preferably, two feedback loops are employed. The firstfeedback loop controls the self-actuated cantilever to maintain arelatively constant force between the tip of the cantilever and thesample surface. The second feedback loop controls the standard Zactuator, at a lower speed than the first feedback loop and serveseither (1) to keep the self-actuated cantilever within its operatingZ-range or (2) to maintain the linearity of the positioning sensitivityof the cantilever when following low frequency topography. Thisembodiment also allows for the standard Z actuator to be exclusivelyused for accurate height measurements when the scan rate is sufficientlylowered, typically less than 500 μm/sec.

According to a preferred embodiment of the present invention, an AFMwhich operates in cyclical mode (i.e., TappingMode™) combines both theAFM Z actuator and the self-actuated cantilever with appropriatefeedback control in a system that oscillates the self-actuated actuatorwithout introducing mechanical resonances other than that of thecantilever. Most notably, the self-actuated cantilever is not oscillatedby vibrating a piezo-crystal mechanically coupled to the cantilever, butrather is oscillated at its resonance by directly exciting thepiezoelectric material disposed thereon. This eliminates mechanicalresonances in the coupling path which would otherwise be present.

As suggested above, the speed of a standard AFM in cyclical mode isgenerally limited by the loop bandwidth of the force detection circuitryand the Z-positioning apparatus. A further limiting factor associatedwith standard AFMs pertains to phase shift contributions from thevarious components of the loop that accumulate to limit the gain of anotherwise stable operating system. Importantly, however, theself-actuated cantilever of the present invention does not havesignificant phase shift contributions at standard operating frequencies,even though the detection bandwidth of the AFM in cyclical mode is stilllimited by the width of the resonance peak of the cantilever. Therefore,the self-actuated cantilever feedback loop is considerably faster thanthe AFM Z-position actuator feedback loop, when both are limited by thesame detection bandwidth. Notably, this embodiment also increases thespeed of the AFM Z actuator feedback loop by providing a larger errorsignal than that which is generated by the cyclical mode amplitudedeflection detector.

In addition, the combination of the standard AFM Z actuator and theself-actuated cantilever allows for greater flexibility in fast scanningcyclical mode. When the Z actuator feedback loop is disabled oroperating with low gain, the topography appears as the control signal tothe self-actuated cantilever. This control signal preferably also servesas the error signal for the AFM Z actuator feedback loop. When the gainof the second feedback loop is optimized, i.e., when the Z actuator isoperating as fast as possible without yielding unreliable output, thetopography then appears in the control signal for the AFM Z-positionactuator. As a result, by incorporating the self-actuated cantileverwithin the control loop, the speed of obtaining highly accuratemeasurements can be increased. Also, as in the previous embodiment, thestandard Z actuator can be used to remove slope or non-linearities fromthe scan in the case in which the self-actuated cantilever follows thetopography of the sample surface. Further, as an alternative to astandard Z actuator such as a piezo-stack actuator, a thermal actuatordisposed on the self-actuated cantilever can be used.

Another preferred embodiment of the invention uses the integratedpiezoelectric element of a self-actuated cantilever to modify the Q ofthe mechanical resonance of the cantilever. In operation, as in theprevious embodiment, the cantilever resonance is excited with theintegrated piezoelectric element, rather than with a mechanicallycoupled driving piezo-crystal. The circuit which provides the cantileverdrive signal modifies the Q of the lever with feedback from the detecteddeflection signal. In particular, the deflection signal is phase shiftedby, preferably, ninety degrees and added back to the cantilever drivesignal. This feedback component of the drive signal modifies the dampingof the cantilever resonance (i.e., active damping) and therebycontrollably decreases or enhances the Q. When modification of thecantilever Q is combined with the structure of the previously describedembodiment wherein the self-actuated cantilever is used forZ-positioning in synchronicity with an AFM Z-position actuator, the scanspeed of the AFM in cyclical mode can be increased by an order ofmagnitude or more.

These and other objects, features, and advantages of the invention willbecome apparent to those skilled in the art from the following detaileddescription and the accompanying drawings. It should be understood,however, that the detailed description and specific examples, whileindicating preferred embodiments of the present invention, are given byway of illustration and not of limitation. Many changes andmodifications may be made within the scope of the present inventionwithout departing from the spirit thereof, and the invention includesall such modifications.

BRIEF DESCRIPTION OF THE DRAWINGS

A preferred exemplary embodiment of the invention is illustrated in theaccompanying drawings in which like reference numerals represent likeparts throughout, and in which:

FIG. 1 is a schematic diagram illustrating an AFM according to thepresent invention including a self-actuated cantilever and feedbackcircuitry to control the cantilever in contact mode operation;

FIG. 2 is a schematic diagram illustrating an AFM according to a secondembodiment of the present invention including a self actuated cantileverand feedback circuitry to control the cantilever in cyclical modeoperation;

FIG. 3 is a schematic diagram illustrating a self-actuated AFMcantilever according to the present invention and a cantilever drivecircuit which modifies the quality factor (“Q”) of the cantilever;

FIG. 4 is a schematic diagram illustrating an AFM according to thepresent invention including a self actuated cantilever and feedbackcircuitry to control the cantilever in cyclical mode, and a cantileverdrive circuit for modifying the quality factor, i.e., Q, of thecantilever; and

FIG. 5 is a perspective view of a probe assembly including aself-actuated cantilever having a thermal actuator integrated therewith.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring to FIG. 1, an AFM 10 according to the present invention, whichis configured for contact mode operation, is shown. AFM 10 includes twofeedback loops 12 and 14 that control an AFM Z-position actuator 16 anda probe assembly 18, respectively. Probe assembly 18 includes aself-actuated cantilever 20 having a tip 26 that interacts with a sampleduring scanning. When scanning in contact mode, tip 26 generallycontinually contacts the sample, only occasionally separating from thesample, if at all. For example, at the end of a line scan tip 26 maydisengage the sample surface. While it scans the surface of the sample,cantilever 20 responds to the output of feedback loop 12 to ultimatelymap the topography of the surface of the sample, as described in furtherdetail below.

Cantilever 20 includes a fixed end 22 preferably mounted to an AFM mount(not shown) and a free distal end 24, generally opposite fixed end 22,that receives tip 26. In operation, the interaction between tip 26 andsample surface 28 causes the deflection of cantilever 20. To measurethis deflection, AFM 10 includes a deflection detector 30 that maypreferably be an optical detection system for measuring the cantileverdeflection by one of the following methods: (1) an optical beam bouncetechnique (see, e.g., Meyer and Amer, “Novel Optical Approach to AtomicForce Microscopy,” Appl. Phys. Lett. 53, 1045 (1988); Alexander,Hellemans, Marti, Schneir, Elings, Hansma, Longmire, and Gurley, “AnAtomic-Resolution Atomic-Force Microscope Implemented Using an OpticalLever,” Appl. Phys. Lett. 65 164 (1989)); (2) an interdigitaldiffraction grating technique (Manalis, Minne, Atalar, and Quate,“Interdigital Cantilevers for Atomic Force Microscopy,” Appl. Phys.Lett., 69 (25) 3944-6 (1996); Yoralioglu, Atalar, Manalis, and Quate,“Analysis and design of an interdigital cantilever as a displacementsensor,” 83(12) 7405 (June 1998)); or (3) by any other known opticaldetection method. These optical-based systems typically include a laserand a photodetector (neither shown) that interact according to one ofthe above techniques. When used in conjunction with very smallmicrofabricated cantilevers and piezoelectric positioners as lateral andvertical scanners, AFMs of the type contemplated by the presentinvention can have resolution down to the molecular level, and canoperate with controllable forces small enough to image biologicalsubstances.

Deflection detector 30 could also be a piezoresistor integrated into thecantilever with an associated bridge circuit for measuring theresistance of the piezoresistor (Tortonese, Barrett, and Quate, “AtomicResolution With an Atomic Force Microscope Using PiezoresistiveDetection,” Appl. Phys. Lett., 62, 8, 834-6 (1993)). Alternatively,deflection detector 30 could be a circuit for measuring the impedance ofthe piezoelectric element of self-actuated cantilever 20, or anothersimilarly related apparatus.

With further reference to FIG. 1, AFM 10 operates at a force determinedby a combination of a first signal having a setpoint value and acantilever detection signal generated by deflection detector 30. Inparticular, AFM 10 includes a difference amplifier 32 that receives andsubtracts the setpoint signal from the cantilever deflection signalthereby generating an error signal. Difference amplifier 32 transmitsthe error signal to a controller 34, preferably a PID(proportional-integral-derivative) controller, of feedback loop 12.Controller 34 can be implemented in either analog or digital, and mayapply either a linear gain or a gain characterized by a more complexcomputation. In particular, controller 34 can apply a gain to the errorsignal that is defined by one or more of a proportional, an integral, ora differential gain.

Controller 34, in response to the error signal, then generates a controlsignal and transmits the control signal to a piezoelectric element 36disposed on self-actuated cantilever 20. By controlling the Z orvertical position of piezoelectric element 36 of cantilever 20 withfeedback control signals from controller 34, AFM 10 ideally operates tonull the error signal generated by difference amplifier 32. When theerror signal is nulled, the force between tip 26 and sample surface 28is maintained at a generally constant value equal to the setpoint. Notethat, optionally, a high voltage amplifier (not shown) may be employedto increase the voltage of the control signal transmitted to cantilever20, but is not required for most applications.

The control signal applied to cantilever 20 by controller 34 of feedbackcircuit 12 is also input, preferably as an error signal, to a secondfeedback circuit 14 such that first feedback circuit 12 is nested withinsecond feedback circuit 14. Feedback circuit 14 includes a secondcontroller 38 which, like controller 34, can be implemented in analog ordigital and may apply either a linear gain or a gain having a morecomplex computation. Controller 38 has a second input to which isapplied a comparison signal having a second setpoint value that is equalto the Z center point of the actuator that it controls, e.g., AFM Zposition actuator 16. Preferably, this setpoint is a zero coordinatevalue, thus making the cantilever control signal (the output ofcontroller 34) itself the error signal. Similar to controller 34,controller 38 (also preferably a PID controller) conditions the errorsignal (i.e., the difference of its input signals) with a gain that ischaracterized by one or more of a proportional, integral, ordifferential gain. Controller 38 generates a second feedback controlsignal that is ultimately applied to Z-position actuator 16 toeffectively null the low frequency components of the control signalgenerated by feedback circuit 12. A high voltage amplifier 40 may beemployed to increase the voltage of the control signal output bycontroller 38 to Z-position actuator 16 and, for most positiontransducers of the scale contemplated by the present invention, such anamplifier 40 is required.

To operate at maximum scanning rate, the gain of the second feedbackloop 14 which controls Z-position actuator 16, is reduced to zero orsome small value. As a result, at a scanning rate greater than about 500μm/sec, the topography of sample surface 28 appears as the feedbackcontrol signal applied to self-actuating cantilever 20 by first feedbackloop 12. In this case, Z position actuator 16 may be controlled in apre-programmed manner to follow the slope of sample surface 28 or toeliminate coupling due to the lateral scanning of tip 26.

Further, in this embodiment, the sensitivity of the self-actuatedcantilever 20 can be calibrated with the standard Z-position actuator16. Sensitivity calibration is accomplished by moving the two actuators16 and 36 in opposite directions to achieve a zero net movement of thetip 26 as measured by force deflection detector 30, and comparing therespective non-zero control signals required to accomplish this zero netmovement.

Turning to FIG. 2, an AFM 50 according to another preferred embodimentof the invention, designed for TappingMode™ or cyclical mode operation,is shown. AFM 50, like the embodiment show in FIG. 1, includes twofeedback circuits (loops) 52 and 54 that respectively controlself-actuated cantilever 20 of probe assembly 18 and AFM Z-positionactuator 16. AFM 50 also includes an oscillator 56 that vibratesself-actuated cantilever 20 by applying an oscillating voltage directlyto piezoelectric element 36 of self-actuated cantilever 20. Theresulting oscillation of the cantilever 20 can be characterized by itsparticular amplitude, frequency, and phase parameters. Note that AFMZ-position actuator 16 is preferably a piezo-tube actuator, and a sampleto be analyzed is disposed on the piezo-tube actuator such that movementof actuator 16 is generally normal to the scanning surface 28 of thesample.

When tip 26 is in close proximity to sample surface 28, the forceinteraction between tip 26 and sample surface 28 modifies the amplitudeof vibration in cantilever 20. Similar to the contact mode embodimentshown in FIG. 1, deflection detector 30 measures the deflection ofcantilever 20 by an optical beam bounce technique, an interdigitaldiffraction grating technique, or by some other optical detection methodknown in the art.

In operation, once detector 30 acquires data pertaining to cantileverdeflection, detector 30 generates a deflection signal which isthereafter converted to an RMS amplitude signal by an RMS-to-DCconverter 58 for further processing by loop 52. Note that,alternatively, lock-in detection, or some other amplitude, phase, orfrequency detection technique may be used as an alternative to RMS-to-DCconverter 58.

The operating RMS amplitude of the cantilever vibration is determined atleast in part by the setpoint value. A difference amplifier 32 subtractsa signal corresponding to the setpoint value from the cantileverdeflection signal output by converter 58. The error signal generated bydifference amplifier 32 as a result of this operation is input tocontroller 34. Controller 34 (again, preferably a PID controller)applies one or more of proportional, integral, and differential gain tothe error signal and outputs a corresponding control signal. Controller34 then applies this control signal to piezoelectric element 36 ofself-actuated cantilever 20 to control the Z-position of cantilever 20as the cantilever traverses varying topography features of the samplesurface. By applying the feedback control signal as described, feedbackloop 52 ultimately nulls the error signal such that, e.g., theoscillation amplitude of cantilever 20 is maintained at the setpointvalue.

A summing amplifier 60 then sums the feedback control signal output bycontroller 34 with the output of driving oscillator 56 so as to applythe feedback cantilever control signal to element 36. Note that a highvoltage amplifier (not shown) may be employed to increase the voltage ofthe summed signal output by amplifier 60 and applied to piezoelectricelement 36 of cantilever 20, but is not required.

The control signal applied to summing amplifier 60 from the controller34 is also input to controller 38 as the error signal of second feedbackloop 54 such that first feedback loop 52 (similar to feedback loop 12 ofthe contact mode embodiment of FIG. 1) is nested within second feedbackloop 54. Controller 38 has a second input that receives a comparisonsignal having a second setpoint value that is equal to the Z centerpoint of the actuator that it controls, e.g., the AFM Z actuator 16.Preferably, this setpoint value is a zero coordinate value such that thecantilever control signal is itself the error signal. Controller 38applies one or more of proportional, integral, and differential gain tothe error signal and outputs a corresponding control signal forcontrolling Z-position actuator 16, and therefore the Z-position of thesample. This control of the Z-position of the sample operates toeffectively null the low frequency components of the self-actuatedcantilever control signal generated by feedback circuit 52. Note that ahigh voltage amplifier 40 may be employed between the output ofcontroller 38 and the input of Z-position actuator 16 to increase thevoltage of the control signal applied by controller 38 to Z-positionactuator 16, and is required for most position transducers of the scalecontemplated by the present invention.

During fast scanning operation, as in the previously describedembodiment, the gain of second feedback loop 54, which controlsZ-position actuator 16, is preferably reduced to zero or some smallvalue. In this cyclical mode case, Z-position actuator 16 may becontrolled, e.g., in a pre-programmed manner, to either follow the slopeof sample surface 28 or to eliminate coupling due to the lateralscanning of tip 26. When the gain of second feedback loop 54 isoptimized, the control signal output by loop 54 is indicative of thesample topography. As a result, depending upon scanning rate, thefeedback cantilever control signals output by loop 52, and correspondingto particular lateral coordinates, are indicative of the topography ofsample surface 28. These signals can then be further processed to createan image of the sample surface.

The bandwidth of the amplitude detection of the cantilever in cyclicalmode or in non-contact mode is limited by the frequency width of themechanical resonance peak of the cantilever, which is defined by the 3dB roll-off frequencies. In particular, the 3 dB roll-off is equal tof/2Q, where f is the center frequency of the resonance peak and Q is thequality factor of the cantilever resonance peak. As such, the width ofthe resonance peak is proportional to the quality factor Q of theresonance peak.

FIG. 3 shows schematically how the Q (quality factor of the cantileverresonance peak) of self-actuated cantilever 20 can be modified using adeflection feedback technique. Generally, an active damping feedback orcantilever drive circuit 62 modifies the oscillating voltage output by adriving oscillator 66 (and applied directly to piezoelectric element 36of cantilever 20) to optimize the bandwidth of amplitude detection.Active damping circuit 62 utilizes a deflection detector 30 that, asdescribed with respect to FIGS. 1 and 2, is preferably an opticaldetection system including a laser and a photodetector, and whichmeasures cantilever deflection by an optical beam bounce technique, etc.Alternatively, as in the previously described embodiments, deflectiondetector 30 could be (1) a piezoresistor integrated into cantilever 20with an associated bridge circuit for measuring the resistance of thepiezoresistor, or (2) a circuit for measuring the impedance of thepiezoelectric element 36 of self-actuated cantilever 20.

When it senses a deflection of cantilever 18, deflection detector 30transmits a corresponding deflection signal to a phase shifter 64 ofactive damping circuit 62. Preferably, phase shifter 64 advances orretards the phase of the sensed deflection signal by ninety degrees.This phase shift acts as a damping component of the oscillatory motionof cantilever 20 to modify the Q of the mechanical resonance of thecantilever. The phase-shifted deflection signal is then summed with theoutput of a driving oscillator 66 by a summing amplifier 68. Prior toapplying the modified oscillating voltage to cantilever 20, an amplifier70 amplifies the output of summing amplifier 68 to a suitable voltagefor driving piezoelectric element 36 of self-actuated cantilever 20.During operation, the output of amplifier 70 drives self-actuatedcantilever 20 at the mechanical resonance of cantilever 18.

The relative gain of the oscillator signal amplitude to the phaseshifted deflection signal determines the degree to which the Q of thecantilever resonance is modified, and therefore is indicative of theavailable bandwidth. Note that the ratio of the two summed signals canbe scaled at summing amplifier 68 to determine the extent to which thecantilever resonance is modified. Alternatively, a gain stage 65 couldbe inserted between phase shifter 64 and summing amplifier 68 to scalethe phase-shifted signal and obtain the resonance modifying data.

In sum, by actively damping the oscillation voltage to modify the Q asdescribed above, damping circuit 62 ideally optimizes the bandwidth ofthe response of the cantilever 20. As a result, the AFM can maximizescan rate, yet still maintain an acceptable degree of force detectionsensitivity.

FIG. 4 shows an AFM 80 according to an alternate embodiment of thepresent invention incorporating the features of AFM 50 (cyclical modeconfiguration—FIG. 2), including two nested feedback loops 82 and 54,with the features of active damping circuit 62 (FIG. 3) to modify the Qof cantilever 20 in fast scanning cyclical mode operation. By activelydamping the resonance of cantilever 20 with feedback signals output bycircuit 62, the force detection bandwidth rises proportionally with acorresponding decrease in the Q. Overall, by combining a decrease in Qwith the control features of AFM 50 (FIG. 2), AFM 80 realizes muchgreater loop bandwidth in cyclical mode, thus achieving much greater(and much more commercially viable) throughput per machine.

Generally, AFM 80 operates as follows. Initially, the deflection signalobtained by deflection detector 30 during a scanning operation is phaseshifted by phase shifter 64 of active damping circuit 62. Preferably, asnoted above, the phase of the deflection signal is advanced or retardedby ninety degrees such that it acts as a damping component of theoscillatory motion of cantilever 20, thus modifying the cantilever Q.The phase-shifted deflection signal is then summed with the output ofoscillator 66 by summing amplifier 68.

The ratio of the two summed signals can be scaled at summing amplifier68 to determine the extent to which the cantilever resonance ismodified. Alternatively, as described in connection with FIG. 3, a gainstage 65 can be inserted between the phase shifter and the summingamplifier to scale the phase-shifted signal. The output of summingamplifier 68 is then further amplified (with amplifier 70) to a suitablevoltage for driving piezoelectric element 36 of self-actuated cantilever20.

With further reference to FIG. 4 and the more specific operation of AFM80, the output of amplifier 70 drives self-actuated cantilever 20 at afrequency equal to that of the natural resonance of cantilever 20,wherein the Q of the driving frequency is modified by active dampingcircuit 62 to increase overall loop bandwidth, and hence increasescanning/imaging speed. Because in this embodiment piezoelectric element36 disposed on cantilever 20 is used to drive cantilever 20 at itsresonant frequency, the oscillating voltage can be applied directly tocantilever 20 without introducing extraneous mechanical resonances intothe system.

When the tip 26 is in close proximity to sample surface 28, the forceinteraction between tip 26 and sample surface 28 modifies the amplitudeof vibration in cantilever 20. The deflection signal generated by thedeflection detector 30 in response to a detected change in the amplitudeof vibration is then converted to an RMS amplitude signal by RMS to DCconverter 58. Notably, lock-in detection or some other amplitude, phase,or frequency detection technique may be used in place of RMS to DCconverter 58.

Similar to AFM 50, the operating RMS amplitude of the cantilevervibration is determined (at least in part) by the setpoint value, whichis subtracted from the cantilever deflection signal by differenceamplifier 32. The error signal generated by difference amplifier 32 isinput to controller 34. Controller 34 applies one or more ofproportional, integral, and differential gain to the error signal andcontrols piezoelectric element 36 of self-actuated cantilever 20 to nullthe error signal, thus ensuring that the amplitude of cantileveroscillation is kept generally constant at a value equal to the setpoint.A high voltage amplifier (not shown) may be employed to increase thevoltage of the signal to cantilever 20, but is not required.

The control signal transmitted by controller 34 to cantilever 20 is alsoinput to controller 38 of second feedback loop 54 such that firstfeedback loop 82 is nested within second feedback loop 54. Preferably,the second setpoint input to controller 38 is a zero value associatedwith AFM actuator 16, in which case the cantilever control signal isitself the error signal conditioned by controller 38. Again, PIDcontroller 38 applies one or more of proportional, integral, anddifferential gain to the error signal for ultimately controllingZ-position actuator 16 to null the low frequency components of thecontrol signal applied to the self-actuated cantilever, when scanning atan optimum rate. Further, as highlighted above, a high voltage amplifier40 may be employed to increase the voltage of the control signal appliedto Z-position actuator 16, and is required for most position transducersof the scale contemplated by the present invention.

In sum, AFM 80 combines an AFM Z actuator 16 with a self-actuatedcantilever 20 in a manner that allows both high speed imaging andaccurate Z-position measurement by decreasing the effective Q ofcantilever 20 with damping circuit 62. Damping circuit 62 activelymodifies the oscillating voltage signal output by oscillator 66, whilepreserving the sensitivity of the natural resonance, to insure that thebandwidth of the cantilever response is optimized. Further, dependingupon the particular sample topography and the scan rate, the topographycan be mapped by monitoring one of the feedback control signalsindependent of the other.

Turning to FIG. 5, an alternate embodiment of the present inventionincludes replacing the standard AFM Z-position actuator 16 (e.g., apiezo-tube actuator) of the previous embodiments with a thermallyresponsive actuator integrated with the self-actuated cantilever. Moreparticularly, the alternate embodiment includes a probe assembly 90including 1) a self-actuated cantilever 92 having a first end 94attached to, e.g., an AFM substrate 107, 2) an elongated portion 96, and3) a second, distal end 97 that includes a tip 98 for scanning thesurface 28 (see, e.g., FIG. 4) of a sample. Self-actuated cantilever 92also includes a Z-positioning element 100 disposed thereon.

This embodiment of the invention operates on the principal of dissimilarexpansion coefficients between cantilever 92, which preferably iscomprised of a silicon material, and the Z-positioning element 100,which is preferably comprised of zinc oxide. In the preferred embodimentof the invention, a thermal actuator, e.g., a resistive heater 104, isintegrated with the cantilever by using, e.g., a doping process.

In operation, by heating the thermal actuator (i.e., the resistiveheater 104), self-actuated cantilever 92 acts as a bimorph.Specifically, the different coefficients of thermal expansion of siliconcantilever 92 and zinc oxide Z-positioning element 100 cause cantilever92 to act as a bimorph when heated. The effect of this response is mostprominent at region 106 of cantilever 92. Notably, similar to theZ-position actuator 16 (piezo-tube Z actuator) of the previousembodiments, probe assembly 90 (and particularly the thermal actuator)can provide highly accurate imaging at relatively low scanning rates.When operating at slower imaging rates (e.g., less than 500 μm/sec), thezinc oxide element 100 is used as a reference for the thermal actuator,the thermal actuator being controlled by the feedback signal from, e.g.,control loop 54 (FIG. 4). Further, the piezoelectric effect of zincoxide Z-positioning element 100 provides fast actuation of thecantilever for faster imaging rates.

Overall, by substituting the thermal actuator for the standard AFMpiezo-tube Z actuator, the vertical range of operation of theself-actuated cantilever is increased, thus providing an effectivealternative for imaging samples that have a topography that demands ahigher range of vertical operation. Whereas the actuator of theself-actuated cantilever of the previously-described embodimentspreferably can cause movement of the cantilever over a rangeapproximately equal to 2-5 μm in the Z-direction and a standard piezotube actuator operates over typically a 5-10 μm range, the thermalactuators shown in FIG. 5 can cause cantilever movement over a rangeapproximately equal to 20-100 μm. Note that, although this alternativeembodiment is described as preferably utilizing zinc oxide as thepiezoelectric element, any material having suitable piezoelectricproperties thus providing Z-positioning of the self-actuated cantilever92, as described herein, can be used.

Although the best mode contemplated by the inventors of carrying out thepresent invention is disclosed above, practice of the present inventionis not limited thereto. It will be manifest that various additions,modifications and rearrangements of the features of the presentinvention may be made without deviating from the spirit and scope of theunderlying inventive concept.

What is claimed is:
 1. An AFM for analyzing a sample at a predeterminedscanning rate in contact mode, the AFM comprising: a self-actuatedcantilever having a Z-positioning element disposed thereon and having atip attached thereto that generally continually contacts the sampleduring a scanning operation; a first feedback circuit that generates acantilever control signal in response to vertical displacement of saidself-actuated cantilever; a second feedback circuit, responsive to saidcantilever control signal, to generate a position control signal,wherein said first feedback circuit is nested within said secondfeedback circuit; and a Z-position actuator, responsive to said positioncontrol signal, to position one of the self-actuated cantilever and thesample to change the spacing between the self-actuated cantilever andthe sample.
 2. An AFM according to claim 1, wherein said Z-positioningelement is a piezoelectric material.
 3. An AFM according to claim 2,wherein said first feedback circuit includes a deflection detector thatdetects the vertical displacement of said self-actuated cantilever andgenerates a corresponding deflection signal.
 4. An AFM according toclaim 3, wherein said first feedback circuit further includes adifferential amplifier that generates an error signal in response tosaid deflection signal.
 5. An AFM according to claim 4, wherein saidfirst feedback circuit further includes a controller that applies a gainto said error signal to generate said cantilever control signal.
 6. AnAFM according to claim 5, wherein said gain is characterized by at leastone of a proportional gain, an integral gain, and a differential gain.7. An AFM according to claim 4, wherein said Z-positioning element isresponsive to said cantilever control signal to cause verticaldisplacement of said self-actuated cantilever so as to generally nullsaid error signal.
 8. An AFM according to claim 3, wherein saiddeflection detector includes a photodetector and a laser.
 9. An AFMaccording to claim 1, wherein the AFM includes a mount, and saidself-actuated cantilever has a first end attached to said mount and asecond, distal end to which bears said tip.
 10. An AFM according toclaim 9, wherein said self-actuated cantilever is responsive to saidcantilever control signal to maintain a generally constant force betweensaid tip and a surface of the sample.
 11. An AFM according to claim 1,wherein said cantilever control signal is indicative of the topographyof the sample.
 12. A method of imaging a sample with a probe-based AFMhaving a self-actuated cantilever and a Z-position actuator, the methodcomprising the steps of: scanning, with the self-actuated cantilever, asurface of the sample at a predetermined scanning rate; detecting adeflection of the cantilever in response to said scanning step andgenerating a corresponding deflection signal; generating, with a firstfeedback circuit, a cantilever control signal in response to saiddeflection signal; applying said cantilever control signal to theself-actuated cantilever to maintain a generally constant force betweenthe self-actuated cantilever and the surface during said scanning step;generating, with a second feedback circuit, a position control signal inresponse to said cantilever control signal wherein said first feedbackcircuit is nested within said second feedback circuit; and applying saidposition control signal to the Z-position actuator to position thesample during said scanning step.
 13. The imaging method of claim 12,wherein said cantilever control signal is indicative of a high frequencytopography feature of the surface.
 14. The imaging method of claim 12,wherein said detecting step is performed using a photodetector and alaser.
 15. The imaging method of claim 14, wherein said detecting stepis performed using one of an optical beam bounce technique and aninterdigital diffraction grating technique.
 16. The imaging method ofclaim 13, wherein the position control signal alone is indicative of thetopography of the sample when said scanning rate is less than 500μm/sec.
 17. The imaging method of claim 13, further including the stepof calibrating the self-actuated cantilever with the Z-position actuatorby using said cantilever control signal to move the self-actuatedcantilever in a first direction and using said position control signalto move the Z-position actuator in a second direction, generallyopposite the first direction, to achieve a zero net movement of theself-actuated cantilever, and then comparing said cantilever controlsignal and said position control signal.
 18. An AFM for analyzing asurface of a sample in cyclical mode, the AFM comprising: aself-actuated cantilever having a Z-positioning element integratedtherewith; an oscillator that oscillates said self-actuated cantilever;a first feedback circuit that generates a cantilever control signal inresponse to vertical displacement of said self-actuated cantileverduring a scanning operation; a second feedback circuit responsive tosaid cantilever control signal to generate a position control signal,wherein said first feedback circuit is nested within said secondfeedback circuit; and a Z-position actuator, responsive to said positioncontrol signal, to position one of said self-actuated cantilever and thesample to change the spacing between the self-actuated cantilever andthe sample; wherein said self-actuated cantilever is responsive to saidcantilever control signal to keep a parameter of probe oscillationgenerally constant.
 19. The AFM according to claim 18, wherein saidoscillator applies an oscillating voltage directly to said Z-positioningelement to oscillate said self-actuated cantilever.
 20. The AFMaccording to claim 19, wherein said Z-positioning element comprises apiezoelectric material.
 21. The AFM according to claim 18, wherein saidposition control signal is indicative of a low frequency component ofthe topography of the surface, and said cantilever control signal isindicative of a high frequency component of the topography of thesurface.
 22. The AFM according to claim 21, wherein the low frequencycomponent includes the slope of the surface topography.
 23. The AFMaccording to claim 18, wherein said cantilever control signal is used tomap the topography of the surface.
 24. An AFM comprising: a firstfeedback loop that outputs a first feedback signal; a self-actuatedcantilever controlled by said first feedback signal; and a Z-positionactuator controlled by a second feedback loop, wherein said firstfeedback loop is nested within said second feedback loop so as to permitsaid second feedback loop to use said first feedback signal as an errorsignal.
 25. A method of imaging a sample in cyclical mode with aprobe-based AFM having a self-actuated cantilever and a Z-positionactuator, the method comprising the steps of: scanning a surface of thesample with the self-actuated cantilever, the self-actuated cantileverincluding a Z-positioning element integrated therewith; generating adeflection signal in response to a deflection of the self-actuatedcantilever during said scanning step; applying an oscillating drivingvoltage to said Z-positioning element to oscillate the self-actuatedcantilever; generating a cantilever control signal in response to saiddeflection signal; maintaining a parameter associated with theoscillation of the self-actuated cantilever at a constant value byservoing the position of the self-actuated cantilever relative to thesample in response to said cantilever control signal; generating aposition control signal in response to said cantilever control signal;and controlling the Z-position actuator in response to said positioncontrol signal.
 26. The imaging method of claim 25, wherein saidcantilever control signal is generated with a first feedback circuit,and said position control signal is generated with a second feedbackcircuit, said first feedback circuit being nested within said secondfeedback circuit, and wherein said second feedback circuit operates at aslower speed than said first feedback circuit.
 27. The imaging method ofclaim 25, wherein the Z-position actuator is a piezo-tube actuator thatcontrols the Z-position of the sample.
 28. The imaging method of claim25, wherein the Z-position actuator is a thermal actuator.
 29. Theimaging method of claim 28, wherein said Z-positioning element compriseszinc oxide and the self-actuated cantilever comprises an elongatedmember made of silicon.
 30. The imaging method of claim 29, furthercomprising the step of heating the self-actuated cantilever to causesaid elongated member to bend in generally a vertical direction.
 31. Theimaging method of claim 30, wherein said heating step is performed usinga heating element disposed on the self-actuated cantilever.
 32. Theimaging method of claim 25, further comprising the step of using saidcantilever control signal to map the topography of the surface.
 33. Amethod of imaging a sample in cyclical mode with a probe-based AFM, themethod comprising the steps of: providing a self-actuated cantilever anda piezo-tube Z-position actuator, said self-actuated cantileverincluding a Z-positioning element integrated therewith; oscillating,with said Z-positioning element, said self-actuated cantilever at acantilever resonant frequency and at a predetermined amplitude ofoscillation; scanning a surface of the sample with said self-actuatedcantilever; generating a deflection signal in response to said scanningstep; generating, with a first feedback loop, a cantilever controlsignal in response to said deflection signal; maintaining said amplitudeof oscillation at a constant value in response to said cantilevercontrol signal; and using said cantilever control signal as an errorsignal in a second feedback loop to control the Z-position actuator,wherein said first feedback loop is nested within said second feedbackloop.
 34. The imaging method of claim 33, wherein said oscillating stepis performed by applying an oscillating voltage directly to saidZ-positioning element.
 35. The imaging method of claim 33, wherein saidcantilever control signal is indicative of the topography of the samplewhen said scanning step is performed at a speed generally greater than500 μm/sec.
 36. A method of analyzing a surface of a sample with a probebased AFM, the method comprising the steps of: providing a self-actuatedcantilever having (1) an elongated member comprised of silicon and (2) aZ-positioning element comprised of zinc oxide; oscillating saidself-actuated cantilever at a cantilever resonant frequency and at apredetermined amplitude of oscillation; scanning the surface with saidself-actuated cantilever; generating a deflection signal in response tosaid scanning step; generating, with a first feedback loop, a cantilevercontrol signal in response to said deflection signal; maintaining saidamplitude of oscillation at a generally constant value in response tosaid cantilever control signal; using said cantilever control signal asan error signal in a second feedback loop to generate a position controlsignal, wherein said first feedback loop is nested within said secondfeedback loop; and heating said self-actuated cantilever in response tosaid position control signal to control the Z-position of saidself-actuated cantilever.
 37. A method of analyzing a sample in cyclicalmode with a probe-based AFM having a self-actuated cantilever and aZ-position actuator, the self-actuated cantilever including aZ-positioning element integrated therewith, the method comprising thesteps of: applying an oscillating driving voltage to said Z-positioningelement to oscillate the self-actuated cantilever and to cause a tip ofthe cantilever to intermittently contact a surface of the sample;generating a deflection signal in response to a deflection of theself-actuated cantilever; generating a cantilever control signal inresponse to said deflection signal; maintaining a parameter associatedwith the oscillating of the self-actuated cantilever at a constant valueby servoing the position of the self-actuated cantilever relative to thesample in response to said cantilever control signal; generating aposition control signal in response to said cantilever control signal;and controlling the Z-position actuator in response to said cantilevercontrol signal.
 38. The method of claim 37, wherein said applying stepcauses the tip to intermittently contact a point on the surface of thesample.
 39. A method of analyzing a sample in cyclical mode with aprobe-based AFM having a self-actuated cantilever and a Z-positionactuator, the self-actuated cantilever including a Z-positioning elementintegrated therewith, the method comprising the steps of: generating adeflection signal in response to a deflection of the self-actuatedcantilever during said scanning step; applying an oscillating drivingvoltage to said Z-positioning element to oscillate the self-actuatedcantilever; generating a cantilever control signal in response to saiddeflection signal; maintaining a parameter associated with theoscillation of the self-actuated cantilever at a constant value byservoing the position of the self-actuated cantilever relative to thesample in response to said cantilever control signal; generating aposition control signal in response to said cantilever control signal;and controlling the Z-position actuator in response to said positioncontrol signal.
 40. An AFM including a cantilever, the AFM comprising: afirst feedback circuit that outputs a first feedback signal to maintaina parameter associated with the operation of the cantilever at asetpoint; and a second feedback circuit, wherein said first feedbackcircuit is nested within said second feedback circuit so as to permitsaid second feedback circuit to use said first feedback signal as anerror signal.
 41. An AFM for analyzing a surface of a sample, the AFMcomprising: a cantilever; a first feedback circuit that generates acantilever control signal in response to vertical displacement of saidcantilever during a scanning operation; a second feedback circuitresponsive to said cantilever control signal to generate a positioncontrol signal, wherein said first feedback circuit is nested withinsaid second feedback circuit; and a Z-position actuator, responsive tosaid position control signal, to position one of said cantilever and thesample to change the spacing between the cantilever and the sample;wherein said self-actuated cantilever is responsive to said cantilevercontrol signal to keep a parameter of cantilever operation generallyconstant; wherein said position control signal is indicative of a lowfrequency component of the topography of the surface, and saidcantilever control signal is indicative of a high frequency component ofthe topography of the surface; wherein the low frequency componentincludes the slope of the surface topography.
 42. The AFM according toclaim 41, wherein said parameter is cantilever oscillation whenoperating the AFM in cyclical mode.
 43. The AFM according to claim 41,wherein said parameter is cantilever deflection when operating the AFMin contact mode.